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Worksheet: Solving Linear Inequalities

Q1:

Write the set of all integer solutions to 4 π‘₯ βˆ’ 8 < βˆ’ 4 .

  • A { 1 }
  • B { βˆ’ 1 , 0 }
  • C { 1 , 0 , βˆ’ 1 , … }
  • D { 0 , βˆ’ 1 , βˆ’ 2 , … }

Q2:

Write the set of all integer solutions to 6 π‘₯ + 3 < βˆ’ 9 .

  • A { βˆ’ 2 }
  • B { βˆ’ 4 , βˆ’ 3 }
  • C { βˆ’ 2 , βˆ’ 3 , βˆ’ 4 , … }
  • D { βˆ’ 3 , βˆ’ 4 , βˆ’ 5 , … }

Q3:

Write the set of all integer solutions to 3 π‘₯ + 2 < 5 .

  • A { 1 }
  • B { βˆ’ 1 , 0 }
  • C { 1 , 0 , βˆ’ 1 , … }
  • D { 0 , βˆ’ 1 , βˆ’ 2 , … }

Q4:

Write the set of all integer solutions to 8 π‘₯ + 4 < βˆ’ 4 .

  • A { βˆ’ 1 }
  • B { βˆ’ 3 , βˆ’ 2 }
  • C { βˆ’ 1 , βˆ’ 2 , βˆ’ 3 , … }
  • D { βˆ’ 2 , βˆ’ 3 , βˆ’ 4 , … }

Q5:

Write the set of all integer solutions to 2 π‘₯ βˆ’ 7 < βˆ’ 9 .

  • A { βˆ’ 1 }
  • B { βˆ’ 3 , βˆ’ 2 }
  • C { βˆ’ 1 , βˆ’ 2 , βˆ’ 3 , … }
  • D { βˆ’ 2 , βˆ’ 3 , βˆ’ 4 , … }

Q6:

Solve . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q7:

Solve . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q8:

Solve . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q9:

Solve . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q10:

Find the solution set of the inequality . Write your answer as an interval.

  • A
  • B
  • C
  • D
  • E

Q11:

The situation where π‘₯ has to be at least 2 away from 1 can be expressed by the compound inequality π‘₯ βˆ’ 1 < βˆ’ 2 or π‘₯ βˆ’ 1 > 2 . Which of the following number lines represents this inequality?

  • A
  • B
  • C
  • D